0
TECHNICAL PAPERS

Modeling Spatial Displacements Using Clifford Algebra

[+] Author and Article Information
Glen Mullineux

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdome-mail: g.mullineux@bath.ac.uk

J. Mech. Des 126(3), 420-424 (Sep 01, 2003) (5 pages) doi:10.1115/1.1701876 History: Received October 01, 2002; Revised September 01, 2003
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Röschel,  O., 1998, “Rational Motion Design—A Survey,” Comput.-Aided Des., 30, pp. 169–178.
Jüttler,  B., and Wagner,  M. G., 1996, “Computer-Aided Design with Spatial Rational B-Spline Motions,” ASME J. Mech. Des., 118, pp. 193–201.
Belta,  C., and Kumar,  V., 2002, “An SVD-Based Projection Method for Interpolation on SE(3),” IEEE Trans. Rob. Autom., 18, pp. 334–345.
Shoemake,  K., 1985, “Animating Rotation with Quaternion Curves,” ACM Siggraph, 19, pp. 245–254.
Fang,  Y. C., Hsieh,  C. C., Kim,  M. J., Chang,  J. J., and Woo,  T. C., 1998, “Real Time Motion Fairing with Unit Quaternions,” Comput.-Aided Des., 30, pp. 191–198.
Ge,  Q. J., 1998, “On the Matrix Realization of the Theory of Biquaternions,” ASME J. Mech. Des., 120, pp. 404–407.
Ge,  Q. J., and Ravani,  R., 1994, “Geometric Construction of Bézier Motions,” ASME J. Mech. Des., 116, pp. 749–755.
Ge,  Q. J., and Ravani,  R., 1994, “Computer Aided Geometric Design of Motion Interpolants,” ASME J. Mech. Des., 116, pp. 756–762.
McCarthy, J. M., 1990, An Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA, p. 130.
Srinivasen,  L. N., and Ge,  Q. J., 1998, “Fine Tuning of Rational B-Spline Motions,” ASME J. Mech. Des., 120, pp. 46–51.
Etzel,  K. R., and McCarthy,  J. M., 1999, “Interpolation of Spatial Displacements Using the Clifford Algebra of E4,” ASME J. Mech. Des., 121, pp. 39–44.
Porteous, I. R., 1995, Clifford Algebras and the Classical Groups, Cambridge University Press, Cambridge, UK.
Lounesto, P., 2001, Clifford Algebra and Spinors, 2nd edition, Cambridge University Press, Cambridge, UK.
Baylis, W. E., ed., 1996, Clifford (Geometric) Algebras with Applications to Physics, Mathematics and Engineering, Birkhauser, Boston.
Lasenby,  J., Fitzgerald,  W. J., Lasenby,  A. N., and Doran,  C. J. L., 1998, “New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation,” Int. J. Comput. Vis., 26, pp. 191–213.
Selig,  J. M., 2000, “Clifford Algebra of Points, Lines and Planes,” Robotica, 18, pp. 545–556.
Mullineux,  G., 2002, “Clifford Algebra of Three Dimensional Geometry,” Robotica, 20, pp. 687–697.
Sobczyk, G., and Bayro-Corrochano, E., eds., 2001, Advances in Geometric Algebra with Applications, Birkhauser Verlag, Boston, USA.
Sommer, G., ed., 2001, Geometric Computing with Clifford Algebra: Theoretical Foundations and Applications in Computer Vision and Robotics, Springer Verlag, Heidelberg, Germany.

Figures

Grahic Jump Location
Bézier motion based on an example in 11
Grahic Jump Location
Differences between the two motions
Grahic Jump Location
Bézier motion through four given positions
Grahic Jump Location
Closed B-spline motion through four given positions

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In